Application limitedness of the model of spheroidal scatterers for describing scattering properties of titanium dioxide

Abstract

The results of measurements of the scattering matrix of an aqueous suspension of titanium dioxide at a wavelength of 0.63 µm in the scattering angle range of 10°-150° are presented. The results of the mea surements are compared with calculation data for scatterers having the shape of prolate ellipsoids. It is shown that, even when the size parameter equals 4, the experimental and calculated values of the matrix elements f 22 and f 12 significantly differ, which is caused by a complex form of TiO 2 particles, and that the determination of the parameters of the distribution of TiO 2 suspension particles in the interpretation of the measurement data in the context of the considered model is possible with an error of 27% in the effective size and 16% in the distribution width.

Retrieval of particle size and shape distributions of TiO2 and BaTiO3 aqueous suspensions using measurement data on the scattering matrix

“…Comparison of measurement results with calculation data for the lognormal size distribution of prolate spheroids and for average values found using microphotographs indicates satisfactory imitation of the scattering properties of these suspensions using the spheroidal model. Thus, for the TiO 2 suspension, using the approximation of the given (lognormal) distribution, theoretical dependences corresponding to the distribution parameters with r av = 0.40 μm and σ = 0.14 μm are the closest to the experimental dependences [12]. We note that the values of r av and σ mentioned above correspond to the parameters of the particle distribution with respect to the area of their projection, r eff and v eff , equal to 0.51 and 0.13 μm, respectively.…”

“…Such a shift is accounted for by the fact that, for particles of irregular shape, the values of f 22 are smaller than those for spheroids with the same size parameter, and to decrease the difference between the values of f 22 , it is necessary to increase the size of the spheroid or to decrease the ratio of the semiaxes. We note that the size distribution obtained by optimization of the function Φ 1 is bimodal and reproduces incorrectly the initial particle distribution, which seems to be caused by additional noticeable deviations of experimental values of nondiagonal elements from those calculated using the model of spheroidal scatterers [12]. Upon retrieval of the ratios of geometrical dimensions of particles, the data obtained by optimizing Φ 3 are the closest to the microscopy data (Fig.…”